A $2$-sphere in $E^{3}$ with vertically connected interior is tame
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- by J. W. Cannon and L. D. Loveland
- Trans. Amer. Math. Soc. 195 (1974), 345-355
- DOI: https://doi.org/10.1090/S0002-9947-1974-0343273-5
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Abstract:
A set X in ${E^3}$ is said to have vertical number n if the intersection of each vertical line with X contains at most n components. The set X is said to have vertical order n if each vertical line intersects X in at most n points. A set with vertical number 1 is said to be vertically connected. We prove that a 2-sphere in ${E^3}$ with vertically connected interior is tame. This result implies as corollaries several previously known taming theorems involving vertical order and vertical number along with several more general and previously unknown results.References
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Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 195 (1974), 345-355
- MSC: Primary 57A10
- DOI: https://doi.org/10.1090/S0002-9947-1974-0343273-5
- MathSciNet review: 0343273